How do I make a Polygon Pattern in Blender?
I'd use a combination of the Displace and Decimate modifiers:

For the above image I used a UV sphere, but you'll notice some stretching at the poles. For this reason I found a icosphere with a high-ish amount of subdivisions (I used 6) works a bit better. I did not use any subsurf for the icosphere.
For the displace texture I used Clouds with a fairly small size (the size you want may vary depending on the size of your object and polygons):
To animate it, set the displace modifier to use another object for the texture coordinates. Add an empty at the center of the sphere and specify it in the displace modifier.

Then animate the scale of the empty:


Dynamic topology sculpting can be used to create this effect with more control, but it may not be very convenient for animation.